JEE Main 2019 (Online) 9th April Morning Slot | Sequences and Series Question 186 | Mathematics

Let the sum of the first n terms of a non-constant A.P., a₁, a₂, a₃, ..... be $$50n + {{n(n - 7)} \over 2}A$$, where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a₅₀) is equal to

(A, 50+45A)

(50, 50+45A)

(A, 50+46A)

(50, 50+46A)

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MCQ (Single Correct Answer)

-1

Out of Syllabus

The sum $$\sum\limits_{k = 1}^{20} {k{1 \over {{2^k}}}} $$ is equal to

$$2 - {11 \over {{2^{19}}}}$$

$$2 - {3 \over {{2^{17}}}}$$

$$1 - {11 \over {{2^{20}}}}$$

$$2 - {21 \over {{2^{20}}}}$$

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MCQ (Single Correct Answer)

-1

If three distinct numbers a, b, c are in G.P. and the equations ax² + 2bx + c = 0 and dx² + 2ex + ƒ = 0 have a common root, then which one of the following statements is correct?

$$d \over a$$, $$e \over b$$, $$f \over c$$ are in G.P.

d, e, ƒ are in A.P

d, e, ƒ are in G.P

$$d \over a$$, $$e \over b$$, $$f \over c$$ are in A.P.

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MCQ (Single Correct Answer)

-1

The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is :

3221

3121

3203

3303